A circuit-preserving mapping from multilevel to Boolean dynamics.

Area of Science:

• Systems Biology
• Computational Biology
• Network Science

Background:

• Boolean models are widely used for biological networks, but often lack the granularity to capture threshold effects.
• Multilevel variables are crucial for accurately representing biological processes, yet their conversion to Boolean models presents challenges.
• Existing conversion methods, like Van Ham's, introduce non-admissible states, complicating analysis of network dynamics and functionality.

Purpose of the Study:

• To develop a new method for converting multilevel biological network models to Boolean models.
• To address the limitations of existing methods, specifically the generation of non-admissible states.
• To preserve the dynamics and interactions of variables in the converted Boolean models.

Main Methods:

• A novel multilevel to Boolean conversion method was developed and implemented in software.
• The method maps each Boolean state to a specific multilevel state, avoiding non-admissible regions.
• The conversion ensures preservation of dynamics and variable interactions, albeit with potentially more complex trajectories.

Main Results:

• The proposed method successfully eliminates non-admissible states, providing a more faithful representation of multilevel models.
• The method was applied to generate a Boolean counter-example to the conjecture that local negative circuits are necessary for sustained oscillations.
• Demonstrated the usability and relevance of the method for analyzing multilevel logical models.

Conclusions:

• The new conversion method offers a significant improvement over existing techniques for analyzing multilevel biological networks.
• By eliminating non-admissible states and preserving dynamics, the method facilitates a deeper understanding of biological circuit functionality.
• This approach has broad implications for the study of complex biological systems and the discovery of novel network properties.